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Simplifying (-7 + 9i)(5 + i) = 0 Multiply (-7 + 9i) * (5 + i) (-7(5 + i) + 9i * (5 + i)) = 0 ((5 * -7 + i * -7) + 9i * (5 + i)) = 0 ((-35 + -7i) + 9i * (5 + i)) = 0 (-35 + -7i + (5 * 9i + i * 9i)) = 0 (-35 + -7i + (45i + 9i2)) = 0 Combine like terms: -7i + 45i = 38i (-35 + 38i + 9i2) = 0 Solving -35 + 38i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -1i)(7 + -9i) = 0Subproblem 1
Set the factor '(-5 + -1i)' equal to zero and attempt to solve: Simplifying -5 + -1i = 0 Solving -5 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1i = 0 + 5 -1i = 0 + 5 Combine like terms: 0 + 5 = 5 -1i = 5 Divide each side by '-1'. i = -5 Simplifying i = -5Subproblem 2
Set the factor '(7 + -9i)' equal to zero and attempt to solve: Simplifying 7 + -9i = 0 Solving 7 + -9i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -9i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9i = 0 + -7 -9i = 0 + -7 Combine like terms: 0 + -7 = -7 -9i = -7 Divide each side by '-9'. i = 0.7777777778 Simplifying i = 0.7777777778Solution
i = {-5, 0.7777777778}
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